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/* mpfr_pow_ui-- compute the power of a floating-point
by a machine integer
Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "mpfr-impl.h"
/* sets x to y^n, and return 0 if exact, non-zero otherwise */
int
mpfr_pow_ui (mpfr_ptr x, mpfr_srcptr y, unsigned long int n, mp_rnd_t rnd)
{
unsigned long m;
mpfr_t res;
mp_prec_t prec, err;
int inexact;
mp_rnd_t rnd1;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (y)))
{
if (MPFR_IS_NAN (y))
{
MPFR_SET_NAN (x);
MPFR_RET_NAN;
}
else if (n == 0) /* y^0 = 1 for any y except NAN */
{
/* The return mpfr_set_ui is important as 1 isn't necessarily
in the exponent range. */
return mpfr_set_ui (x, 1, rnd);
}
else if (MPFR_IS_INF (y))
{
/* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
if ((MPFR_IS_NEG (y)) && ((n & 1) == 1))
MPFR_SET_NEG (x);
else
MPFR_SET_POS (x);
MPFR_SET_INF (x);
MPFR_RET (0);
}
else /* y is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (y));
/* 0^n = 0 for any n */
MPFR_SET_ZERO (x);
MPFR_RET (0);
}
}
else if (MPFR_UNLIKELY (n <= 2))
{
if (n < 1)
/* y^0 = 1 for any y */
return mpfr_set_ui (x, 1, rnd);
else if (n == 1)
/* y^1 = y */
return mpfr_set (x, y, rnd);
else
/* y^2 = sqr(y) */
return mpfr_sqr (x, y, rnd);
}
/* MPFR_CLEAR_FLAGS useless due to mpfr_set */
MPFR_SAVE_EXPO_MARK (expo);
prec = MPFR_PREC (x);
mpfr_init2 (res, prec + 9);
rnd1 = MPFR_IS_POS (y) ? GMP_RNDU : GMP_RNDD; /* away */
do
{
int i;
prec += 3;
for (m = n, i = 0; m; i++, m >>= 1)
prec++;
/* now 2^(i-1) <= n < 2^i */
mpfr_set_prec (res, prec);
err = prec <= (mpfr_prec_t) i ? 0 : prec - (mpfr_prec_t) i;
MPFR_ASSERTD (i >= 1);
/* First step: compute square from y */
inexact = mpfr_sqr (res, y, GMP_RNDU);
if (n & (1UL << (i-2)))
inexact |= mpfr_mul (res, res, y, rnd1);
for (i -= 3; i >= 0; i--)
{
inexact |= mpfr_sqr (res, res, GMP_RNDU);
if (n & (1UL << i))
inexact |= mpfr_mul (res, res, y, rnd1);
}
/* Check Overflow (can't use MPFR_GET_EXP since there can be an INF )*/
if (MPFR_UNLIKELY (MPFR_IS_INF (res)
|| MPFR_EXP (res) >= __gmpfr_emax))
{
mpfr_clear (res);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_set_overflow (x, rnd,
(n % 2) ? MPFR_SIGN (y) : MPFR_SIGN_POS);
}
/* Check Underflow (can't use MPFR_GET_EXP since there can be a ZERO )*/
if (MPFR_UNLIKELY (MPFR_IS_ZERO (res)
|| MPFR_EXP (res) <= __gmpfr_emin))
{
mpfr_clear (res);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_set_underflow (x, rnd,
(n % 2) ? MPFR_SIGN(y) : MPFR_SIGN_POS);
}
}
while (inexact && !mpfr_can_round (res, err, GMP_RNDN, GMP_RNDZ,
MPFR_PREC(x) + (rnd == GMP_RNDN)));
inexact = mpfr_set (x, res, rnd);
mpfr_clear (res);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (x, inexact, rnd);
}
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